A force is applied to a steel wire 'A', rigidly clamped at one end… | JEE Main 2023 (30 Jan, Shift 2)

Q13JEE Main 2023 · 30 JAN · SHIFT 2Easy

Young's Modulus & Elongation

A force is applied to a steel wire 'A', rigidly clamped at one end. As a result elongation in the wire is $0.2\text{ mm}$ . If same force is applied to another steel wire ' $B$ ' of double the length and a diameter $2.4$ times that of the wire ' $A$ ', the elongation in the wire ' $B$ ' will be (wires having uniform circular cross sections)

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Answer: (a)

Same material and force: $\Delta L \propto \frac{L}{d^2}$
$\Delta L_B = 0.2 \times \frac{2}{(2.4)^2} = \frac{0.4}{5.76}\ \text{mm}$
$\Delta L_B \approx 0.069\ \text{mm} = 6.9 \times 10^{-2}\ \text{mm}$
So the answer is (a).

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